Zero Correlation Zone Research Articles

Polyphase Scrambled Walsh Codes for Zero-Correlation Zone Extension in QS-CDMA

Polyphase complex scrambling patterns are designed to extend the zero-correlation zone (ZCZ) of a family of user spreading sequences, called properly scrambled Walsh-Hadamard (PSW) codes, recently proposed for quasi-synchronous (QS) code-division multiple-access systems. The merits of the binary (ZCZ equals 2) and quadri-phase (ZCZ equals 4) PSW codes over the existing QS spreading codes are still retained in the proposed polyphase PSW codes. Scrambling patterns for the case of ZCZ of 8 are derived first. Then, the scrambling pattern design rules are generalized for greater ZCZs and a structured procedure to generate polyphase PSW codes for any ZCZ is developed. Finally, the cross-correlation properties of the proposed spreading codes are evaluated.

Phase Coded Waveform Design for Sonar Sensor Network

Since it is known that interference with each sonar sensor could be effectively reduced when waveforms are appropriately designed for a Sonar Sensor Network (SSN), we provide a set of new ternary codes called optimized punctured Zero Correlation Zone sequence-pair set (ZCZPS) and provide a method to construct such codes. We study the codes' properties especially using the ambiguity function to analyze the nature of the output of the matched filter. We apply our provided ternary codes to the SSN as pulse compression codes for narrowband pulse signals and simulate the target detection performance of the system. Comparing with the classical periodic Gold sequences, our codes could improve the system detection performance.

Constructions of binary array set with zero-correlation zone

Based on the perfect binary array and the orthogonal matrix, a new method of constructing zero-correlation zone binary array set is proposed, yielding binary array sets with member sizes almost achieve the theoretical upper bound. A recursive construction of zero-correlation zone binary array set is also proposed and the obtained array sets have even larger sizes as well as additional good correlation properties.

Constructions of Binary and Quaternary Periodic Complementary Sequence Sets with Zero Correlation Zone

摘要: 该文基于二元周期互补序列集，研究了二元和四元零相关区(ZCZ)周期互补序列集的构造方法。利用移位序列和交织法来构造二元ZCZ周期互补序列集，序列集的零相关区长度可以灵活设定。利用逆Gray映射构造了四元ZCZ周期互补序列集，零相关区长度同样可以灵活设定。如果采用的初始周期互补序列集参数达到理论界限，得到的二元和四元ZCZ周期互补序列集参数都是可以达到理论界限的。 关键词: 周期互补序列 / 零相关区(ZCZ) / 交织法 / 逆Gray映射 / 移位序列

A Generalized Construction Scheme of a Zero-Correlation Zone Sequence Set with a Wide Inter-Subset Zero-Correlation Zone

A Generalized Construction Scheme of a Zero-Correlation Zone Sequence Set with a Wide Inter-Subset Zero-Correlation Zone

A construction of inter-group complementary codes with flexible ZCZ length

A general construction of inter-group complementary (IGC) codes is proposed based on perfect complementary (PC) codes, interleaving operation, and the orthogonal matrix. The correlation properties of the newly constructed IGC codes can be described as follows: (1) the autocorrelation sidelobes of the codes are zeros in the zero correlation zone (ZCZ); (2) the cross-correlation functions (CCFs) between any two different codes of the same group are zeros in the ZCZ; (3) the CCFs between any two codes of different groups are zeros everywhere. The key point of this construction is that the ZCZ length of the generated IGC codes can be chosen flexibly. It is well known that there is a limitation between the ZCZ length and the number of mates; that is, the smaller is the length of ZCZ, the more are the IGC codes that can be generated. Therefore, if we can choose the ZCZ length of the IGC codes flexibly according to the requirement of the system, more users can be accommodated in the system.

Study on the Recursive Constructions of Zero Correlation Zone Array Pairs Set

Study on the Recursive Constructions of Zero Correlation Zone Array Pairs Set

Construction of Ternary Sequence Sets with Aperiodic Zero Correlation Zone

摘要: 该文基于任意两个NN Hadamard矩阵，构造出一类三元非周期零相关区序列集。与Donelan和OFarrell的构造方法相比，该文构造出的序列具有较高的能量效率。又进一步构造出两个相互正交的具有非周期零相关区的三元序列集，这样就可以提供更多的能够在准同步CDMA系统中使用的序列。 关键词: 准同步CDMA系统 / 零相关区序列集 / Hadamard矩阵 / 相互正交序列集

Novel Scheme of Multi-Rate Quasi-synchronous Coherent Time-spreading OCDMA System

Abstract We propose a novel scheme of multi-rate quasi-synchronous coherent time-spreading OCDMA system, employing orthogonal variable spreading factor (OVSF) codes with a zero-correlation zone. Within permissible time delay, the aperiodic cross-correlation of OVSF with a zero-correlation zone equals zero. Therefore, multiple-access interference and beat noise can be removed in multirate quasi-synchronous coherent time-spreading OCDMA system, and the near-far problem can also be eliminated. Simulation of eight simultaneous users with 2.5 Gbit/s, 1.25 Gbit/s and 0.625 Gbit/s is demonstrated, where the fiber link consists of 20 km single-mode fiber, plus 2 km Dispersion Compensating Fiber. The results show that OVSF codes with a zero-correlation zone can be employed to multi-rate quasi-synchronous coherent time-spreading OCDMA system.

16-QAM Sequences with Zero Correlation Zone from the Known Quadriphase ZCZ Sequences

Based on the known quadriphase zero correlation zone (ZCZ) sequences ZCZ4(N,M,T), four families of 16-QAM sequences with ZCZ are presented, where the term “QAM sequences” means the sequences over the quadrature amplitude modulation (QAM) constellation. When the quadriphase ZCZ sequences employed by this letter arrive at the theoretical bound on the ZCZ sequences, and are of the even family size M or the odd width T of ZCZ, two of the resulting four 16-QAM sequence sets satisfy the bound referred to above. The proposed sequences can be potentially applied to communication systems using 16-QAM constellation as spreading sequences so that the multiple access interference (MAI) and multi-path interference (MPI) are removed synchronously.

A General Construction of ZCZ Sequence Set with Large Family Size and Long Period

In this paper, we introduce a new general construction of zero correlation zone (ZCZ) sequence set, which is based on two given ZCZ sequence sets. Compared with the two given sequence sets, the resultant sequence set not only has larger family size and longer period, but also provides more flexible choices of basic sequences, ZCZ length and family size.

Construction of Binary Array Set with Zero Correlation Zone Based on Interleaving Technique

Sequences with good correlation properties are of substantial interest in many applications. By interleaving a perfect array with shift sequences, a new method of constructing binary array set with zero correlation zone (ZCZ) is presented. The interleaving operation can be performed not only row-by-row but also column-by-column on the perfect array. The resultant ZCZ binary array set is optimal or almost optimal with respect to the theoretical bound. The new method provides a flexible choice for the rectangular ZCZ and the set size.

Orthogonal and ZCZ Sets of Real-Valued Periodic Orthogonal Sequences from Huffman Sequences

This paper presents a method of generating sets of orthogonal and zero-correlation zone (ZCZ) periodic real-valued sequences of period 2n, n ≥ 1. The sequences admit a fast correlation algorithm and the sets of sequences achieve the upper bound on family size. A periodic orthogonal sequence has the periodic autocorrelation function with zero sidelobes, and a set with orthogonal sequences whose mutual periodic crosscorrelation function at zero shift is zero. Similarly, a ZCZ set is the set of the sequences with zero-correlation zone. In this paper, we derive the real-valued periodic orthogonal sequences of period 2n from a real-valued Huffman sequence of length 2ν + 1, ν being a positive integer and ν ≥ n, whose aperiodic autocorrelation function has zero sidelobes except possibly at the left and right shift-ends. The orthogonal and ZCZ sets of real-valued periodic orthogonal sequences are useful in various systems, such as synchronous code division multiple access (CDMA) systems, quasi-synchronous CDMA systems and digital watermarkings.

A Ternary Zero-Correlation Zone Sequence Set Having Wide Inter-Subset Zero-Correlation Zone

The present paper introduces a novel construction of ternary sequences having a zero-correlation zone. The cross-correlation function and the side-lobe of the auto-correlation function of the proposed sequence set is zero for the phase shifts within the zero-correlation zone. The proposed sequence set consists of more than one subset having the same member size. The correlation function of the sequences of a pair of different subsets, referred to as the inter-subset correlation function, has a wider zero-correlation zone than that of the correlation function of sequences of the same subset (intra-subset correlation function). The wide inter-subset zero-correlation enables performance improvement during application of the proposed sequence set. The proposed sequence set has a zero-correlation zone for periodic, aperiodic, and odd correlation functions.

A Generalized Construction of Zero-Correlation Zone Sequence Set with Sequence Subsets

The present paper introduces a new approach to the construction of a sequence set with a zero-correlation zone for both periodic and aperiodic correlation functions. The proposed sequences can be constructed from a pair of Hadamard matrices of orders n0 and n1. The constructed sequence set consists of n0n0 ternary sequences, each of length n0(m+2)(n1+Δ), for a non-negative integer m and τ≥2. The zero-correlation zone of the proposed sequences is $|\\ au|\\le \\ablen^{m+1}-1$, where τ is the phase shift. The proposed sequence set consists of n0 subsets, each with a member size n1. The correlation function of the sequences of a pair of different subsets, referred to as the inter-subset correlation function, has a zero-correlation zone with a width that is approximately τ times that of the correlation function of sequences of the same subset (intra-subset correlation function). The inter-subset zero-correlation zone of the proposed sequences is $|\\ au|\\le \\slen\\ablen^{m+1}$, where τ is the phase shift. The wide inter-subset zero-correlation enables performance improvement during application of the proposed sequence set.

Construction of Mutually Orthogonal Zero Correlation Zone Polyphase Sequence Sets

In this paper, two constructions of mutually orthogonal zero correlation zone polyphase sequence sets are presented. The first one is based on DFT matrices and interleaving iteration. After each recursive step, the period of sequence and the length of zero-correlation zone are two times larger than that in the last step. The second method, based on DFT matrices and orthogonal matrices, can generate numbers of mutually orthogonal optimal ZCZ sequence sets whose parameters reach the theoretical bounds by using interleaving and shifting techniques. As a result, the algorithms proposed can provide more sequences for the QS-CDMA (quasi-synchronous CDMA) systems.

16-QAM Sequences with Zero Correlation Zone from the Known Binary ZCZ Sequences and Gray Mapping

16-QAM Sequences with Zero Correlation Zone from the Known Binary ZCZ Sequences and Gray Mapping

Recursive algorithm to directly obtain the sum of correlations in a CSS

This paper presents a new recursive algorithm to directly obtain the sum of the autocorrelation functions of the M sequences belonging to a Complementary Set of Sequences (M-CSS). The proposed algorithm allows a digital filter with only one stage to be obtained, what significantly reduces the total number of memory requirements, multiplications and additions to be performed in comparison with the use of M correlators, even when these correlators could have an efficient implementation. The use of this algorithm can be of great relevancy since there is an increasing interest in the use of CSS (or derived sequences such as Loosely Synchronized—LS-sequences or Zero Correlation Zone—ZCZ-sequences) in the field of communications and sensor systems.

Constructions of ZCZ Array Pairs Set by Interleaving Techniques

By using shift sequence set, a new construction of ZCZ (Zero Correlation Zone) array pairs set is proposed. Compared with known results, the obtained ZCZ array pair sets include more array pairs. For computing the size of zero correlation zone, the difference matrix of shift sequence set is introduced. Furthermore, more constructions of shift sequences are presented. The proposed technique can be used to construct the ZCZ punctured arrays set.

A Simple Method for Generating Optimal ${\rm Z}$-Periodic Complementary Sequence Set Based on Phase Shift

In this letter, we introduce a simple approach to generate Z-periodic complementary set (ZPCS) by performing phase shift operation on periodic complementary sequence set (PCS). Favorable correlation properties of ZPCS enable its applications not only in MIMO channel estimation as optimal training sequences, but also in MC-CDMA system as spreading sequences to efficiently handle multipath interference (MI) and multiple access interference (MAI). Our approach provides flexible choices for zero correlation zone (ZCZ) length and set size. The resultant ZPCS is optimal with respect to the theoretical bound.